Digital Signal Processing: System Analysis and Design

9.11: Filter Banks and Wavelets with MATLAB

9.11 Filter Banks and Wavelets with MATLAB

The functions described below are from the MATLAB Wavelet toolbox. This toolbox includes many pre-defined wavelets, divided into families. For example, among others we have the Daubechies, the biorthogonal, the Coiflet and the Symmlet families (Mal-lat, 1998). Most functions require the desired wavelet in a family to be specified. The functions which involve wavelet transform computation also permit the specification of the filter bank coefficients.

  • dyaddown: Dyadic downsampling.

    Input parameters:

    • The input vector or matrix x;

    • The integer evenodd; if evenodd is even, the output corresponds to the even samples of the input; if evenodd is odd, the output corresponds to the odd samples of the input;

    • The parameter 'type', when x is a matrix; if 'type'='c', only the rows are downsampled; if 'type'='r', only the columns are downsampled; if 'type'='m', both rows and columns are downsampled;

    Output parameter: The vector or matrix y containing the downsampled signal.

    Example:

    x=[1.0 2.7 2.4 5.0]; evenodd=l;y=dyaddown(x,evenodd);
  • dyadup: Dyadic upsampling.

    For a complete list of input and output parameters, see command dyadown.

    Example:

    x=[0.97 -2.1 ; 3.7 -0.03]; evenodd=0;y=dyadup(x,'m',evenodd);
  • qmf: Generates a quadrature mirror filter of the input.

    Input parameters:

    • The input vector or matrix x;

    • The integer p. If p is even, the output corresponds to x in reversed order with the signs changed for the even index entries. If p is odd, the output corresponds to

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